Method and apparatus for balancing rotating members



Feb. 5, 1946. E. w. REYNOLDS 2,394,482

METHOD AND APPARATUS FOR BALANCING ROTATING MEMBERS Filed Oct. 9, 1941FIG. I

INVENTOR E. W. REYNOLDS ATTORNEY Patented F eb. 5, 1946 METHOD APPARATUSFOR BALANCING ROTATING MEMBERS Ellwood W. Reynolds, Wcstfleld, N. J.,assignor to Western Electric Company, Incorporated, New York, N. Y., acorporation of New York Application October 9, 1941, Serial No. 414,269

4Claims.

This invention relates to balancing rotating members, and moreparticularly to a method and means for measuring the effect of, andcompensating for, a new and heretofore unknown type of unbalance in arotating member.

1n the .manufacture of certain kinds of cable it may be desired to wrapa tape or other strandit may be of paper, textile material, rubber orrubber compound, metal, or other substance as the case may be-about a,cable core. To this end the core is caused to advance longitudinally,while a supply of the strand material, e. g. paper tape, is caused torevolve about the advancing core in a stationarily located orbit havingthe core substantially in its axis. In some instances this supply is aso-called pad of paper tape, i. e. a flat circular mass of tape wound onitself solidly in spiral turns or convolutions. Such a pad is ordinarilysupported on a flat, relatively thin, coaxial, circular disc of suitablematerial, usually metal. The supporting disc is mounted to be freelyrotatable on its' own axis (and so on the axis of the pad supported onit) in a frame which in turn is rotatable about an axis at right anglesto the axis of the disc. The core to be wound advances longitudinallyalong the axis of rotation of the frame. The frame is driven in rotationabout the core and thus carries the disc and its pad in a circular orbitabout the core and in a plane at right angles thereto and to the axis ofthe frame. The outer end of the tape composing the pad is ledtangentially from the circular pad through suitable guides to the coreand is served thereon by the combined action of the longitudinal advanceof or other strand being drawn off at high speed thecore and therevolution of the pad in its orbit about the core. It results also thatthe tape is drawn tangentially from the pad and thus causes the pad andtherewith its supporting disc -to rotate on their common axis in theframe while at the same time they are revolving with the frame about theaxis of the frame. It will be at once evident to anyone familiar withsuch mechanical motions and relations generally, that if such apparatusis to be run at any speed, questions of statical and dynamicalrotational balance and of gyroscopic forces and stresses will arise. Inthe past these difiiculties have been satisfactorily overcome by knownmeans, the difficulties and their remedies being generally wellunderstood. However, applicant has discovered that, when speeds ofoperation are attempted which are considerably above those heretoforecontemplated in practice, a new and apparently not heretofore recognizedperiodic disturbance be severely jerked or even ruptured.

An object of the present invention is to provide a method for balancin arotatable member by rotatively supporting the member on its axis,rotating this axis about another axis transverse thereto, measuring thetendency of the member to rotate about its own axis as a result of therotation'about the transverse axis, and compensating the member inaccordance with the measurement to remove this tendency.

Another object is to provide an apparatus for effecting the abovementioned rotation and meas--. urement.

Other objects and features of the invention will appear from thefollowing detailed description of one embodiment thereof taken inconnection with the accompanying drawing, in which the same referencenumerals are applied to identical parts in the several figures and inwhich Fig. 1 is a, partly diagrammatic view in side elevation of anapparatus for serving paper tape on a longitudinally advancing cablecore;

Fig. 2 is a-diagrammatic view of an assembly of elements to illustratethe principle of the invention;

Fig. 3 is a similar view of another illustrative assembly;

Fig. 4 is a similar view of a third form thereof;

Fig. 5 is a similar view of a fourth form thereof;

Fig. 6 is a similar view of an apparatus for determining the angularposition and excess mass of the master diameter of a member; and

Fig. '7 is a section on the line 1-1 of Fig. 6.

In Fig. 1 there are shown the essentials of an apparatus for servingpaper tape on a cable core. The core 19 is advanced longitudinally fromleft to right, by suitable means not shown, through the axially hollowbearings or journals of a frame 20 rotatable about and substantiallycoaxial with the advancing core. Identically similar discs 2| aremounted in the frame diametrically opposite each other, in such wise asto be rotatable each about a central axis perpendicular to its disc andalso perpendicular to the axis of the frame 20. Identically similar pads22 of paper tape l8 are supported on the two discs 2|. The tapes l8 areled from the pads 22 through identically symmetrical paths and overidentically similar guide members to opposite sides of the same portionof the core and are there served thereon by the combined action of thelinear longitudinal advance'of the core and the orbital motion of thepads around the core, the frame being driven in rotation, to effect thislast, by means not shown.

Assuming now that all difficulties due to statical unbalance, dynamicalunbalance, and gyroscopic forces and stresses have been met and overcomein .ways generally familiar, the apparatus described will operate in anentirely satisfactory manner at all speeds within the ranges heretoforeused. But when certain higher speeds are attempted to be employed, aheretofore unknown and peculiar difiiculty arises. There appears whatseems to be a periodic jerkiness in the motion of the discs 2I abouttheir individual axes of rotation, which manifests itself in aperiodically rising and falling resistance to the withdrawal of tape,Evidently at these higher speeds some heretofore negligible forcebecomes sufficiently great to make itself felt, alternately retardingand accelerating the rotary motion of the discs which is primarily dueto the tangential pull of the tapes being withdrawn from the padssupported on the discs.

The discs 2I in the apparatus in which the phenomenon first appearedwere made with all care. Each was geometrically symmetrical in formabout its center. When tested in the ordinary way by rotation about astationary axis each was found to be in substantially perfect static anddynamic rotary balance, The effect could not be accounted for byaccepted gyroscopic forces.

After much study and experiment a theory was formulated which appearedto account for the observed phenomena and pointed out a success- I fulmethod for obviating the diificulty, and for producing rotary memberswhich are not afiected by the periodic disturbance described, even athigh speeds operation.

Consider now Fig. 2, in which a shaft 30 is horizontally journalled instationary bearings 3| and can be driven by a pulley 32 and belt 33, Abar 34 of uniform cross section and density is pivoted as shown on,atransverse pin 35 at its mid-point and is carefully adjusted to be inexact balance about its pivot 35.- So long as the shaft 30 isstationary, the bar 34 will remain in whatever position it may be placedangularly with respect to the shaft. But if the shaft 30 be rotated andthus twirls the bar about the shaft, the bar tends to set itself atright angles to the shaft in the position shown in dotted lines. This isbecause each half of the bar tends to move outwardly under centrifugalforce as indicated by the arrows drawn from the respective centers ofgravity of the two arms of the bar. This creates a couple tending toturn the bar clockwise from the posit on shown toward the dotted lineposition in which the couple disappears and the bar remains.

Assume now that a circular disc I 34 of flat sheet metal be pivoted atits center on the pin 35, as in Fig. 3, in place of the bar 34, and thatthe disc is carefully adjusted, as by filing its edge delicately, untilit shows no tendency to rotate on the pin no matter how it is turned, i.e. so that it is in accurate balance about the pin on all diameters.Then, if the shaft 30 be rotated, it will usually be found that the discwill rotate in one direction or other on its pivot until a particulardiameter stands perpendicular to the shaft 30. If one or bothextremities of this diameter be marked as by tiny dots of ink, it willbe found that the same diameter always sets itself at right angles tothe axis of the shaft 30 when the shaft is rotated, although the discremains in whatever position it is placed when the shaft is stationary.Now if material be removed from the disc in equal masses from two pointsalong this master diameter which are on opposite sides of the, pivot 35and at equal distances therefrom,

obviously neither the static nor dynamic balance already existing isaltered in any way. Nevertheless, by cut and try, a state can beattainedin this. fashion in which the "master diameter loses itspreeminence, and the disc I34 no longer tends to turn about the pin 35when the shaft 30 is rotated, but remains in whatever angular positionrelative thereto it was when rotation began.

If the correction just described, however, be carried too far, someother diameter of the disc will assume the role of master and insistupon placing itself at right angles to the shaft 30 when this isrotated.

The correction to remove this master" char:

acter of any diameter in which it appears may also be accomplished byadding equal masses at two points of the diameter at right angles to themaster diameter, the two points of mass accretion being equidistant fromthe axis of the pin 35 and on opposite sides of the pin.

Obviously, considering Fig. 2 and its bearing on Fig. 3, when the shaft30'of Fig. 3 is rotated, every diameter of the disc I34 must strive toset itself at right angles to the shaft. If the effective massdistributed along any diameter is greater than that along any otherdiameter, this most massive of all the diameters become the "master" andsets itself at right angles to the shaft. Conversely, if a masterdiameter appears, it is because a greater mass is distributed along thatdiameter than along any other diameter. Hence its master character canbe destroyed either by diminishing theeflective mass along it, or byincreasing the eifective mass along the diameter at right angles to it,or by a combination of both methods, care being taken to modify the massalong the diameter spect to its center.

Substantially the same general phenomena arise in the case of sucharrangements as are shown in Figs. 4 and 5 (if air resistance eifects beexcluded in the case of Fig. 4, which may otherwise more or less annulor complicate the effects here in question). The fact that the plane ofrotation of the bar 34 in Fig. 4 or of the disc I34 in Fig. 5 does notpass through the axis of the shaft 30, does not alter the masterdiametereffect discussed above in connection with Figs. 2 and 3. The bar 34 ordisc 3 I34 in being revolved once about the axis of the shaft 30 in Fig.4 or Fig. 5 is also, in efiect, compelled to rotate once about an axisthrough its center parallel to the xis of the shaft 30. Hence the masterdiameter efiect" appears in Fig. 4 or Fig. 5 in the same sense and valueas in Fig. 2 or Fig. 3 respectively.

A moment's consideration of Fig. 4 and of the disc 2| in Fig. 1 willshow that they are substantially the same arrangement, since the discsupport 2I is rotatable about an axis which is at right angles to theaxis of the frame 20 about which the support 2I' is revolved by themotion of the frame. Hence if there bea master diameter in the disc 2 I,it will tend to set itself at right angles to the principal plane of theframe, 20, and to resist being forced out of that position. But the disc2I is being driven in rotation about its own axis .by withdrawal of tapefrom e Dad 22 tobe symmetrically with reassess:

wound on the core II. If, at any given moment, the master diameter ofthe disc 2| chance to be at right angles to the frame 20, the masterdiameter' effect will oppose rotation of the disc during the next ninetydegrees, i. e. until the master diameter comes to lie in the plane ofthe frame, at which instant the effect becomes zero. During the nextninety degrees, the effect tends to aid the rotation ofthe disc untilthe master diameter is again perpendicular to the plane of the frame.Thus this cycle of alternately opposing and assisting the rotationenforced by withdrawal of tape recurs twice in every rotation of thedisc, and produces the periodic disturbance of the motion of the discwhich may in practise, with high speeds of operation, become greatenough to cause the tape to be ruptured.

Probably no piece of material from which a disc 2| is to be made, can befound, whether cast. molded, forged, rolled or otherwise made, which isso truly homogeneously uniform in microstructure and density, that amaster diameter will not appear at sufliciently high speeds ofrevolution and rotation, no matter how accurately the disc is formed andbalanced for static and dynamic symmetry. Indeed, a disc may be inperfect rotational balance so far as static and dynamic rotationalerrors are concerned and still be affected with variations of density,symmetrical radially with respect to the center while varying around thecircumference of a circle ithin the disc and concentric with the disc.

To illustrate the order of magnitude or the quantities in question, thefollowing are taken from a case in actual practise. A disc 2| was madeof metal and carefully balanced statically and dynamically. It was aboutthirteen and onehalf inches in diameter, one inch thick at its hub,one-eighth inch thick at its rim, had a plane upper surface, had twelveequi-spaced radial ribs on its under, conical face, and weighed aboutfive pounds. In operation the frame carrying it revolved at speeds fromzero up to 500 R. P. M., while the maximum speed of rotation of the disc(maximum when the pad of tape on it was about used up) Variedproportionally from zero to 120 R. P. M. In this particular case, themaster diameter effect became perceptible at about 200 R. P. M.revolution and 48 R. P. M. rotation, while at 500 R. P. M. revolutionand 120 R. P. M. rotation, the effect was fatal to the tape whichruptured.

Experiment proved that at 1500 R. P. M. revolution, the maximum momentof the master diameter, with the master diameter at forty-five degreesto the frame axis, was about twenty-five inch pounds. Hence a periodicvariation in tape tension of the order of thirty-three pounds would becaused by the master diameter effect in this disc at 1500 R. P. M.revolution speed.

On correcting the disc by adding mass in a total amount of about two andone-half ounces distributed symmetrically along the diameter at rightangles to the master diameter, the disc could be operated withoutaffecting the tape harmfully at 1500 R. P. M. revolution and 320 R. P.M. rotation. In fact these maximum prac ticable speeds were not limitedby the master diameter effect, which was negligible, but by otherfactors having no relation thereto.

In order to determine the position of the master diameter and the valueof its effective excess mass in a disc such as 2|, or in any analogouscentrally symmetrical, i. e. statically and dynamically balanced, memberadapted for simultaneous rotation and revolution about non parallelaxes, an apparatus was designed as diagrammatically illustrated in Figs.6 and'l. Here a frame 4| statically and dynamically balanced withrespect to coaxial stub shafts 4| and 42, is rotatablyiournalled insupports 43 and can be revolved by a pulley 44 and belt 45. A transverseshaft 48 is removably mounted in the frame 40 aligned at right angles tothe axis of rotation of the frame and freely rotatable in its hearingsin the frame with respect thereto. The central portion of the shaft isformed with a screw thread 41 on which are engaged opposed clamp nuts 48and 49. These nuts are preferably faced with rubber or other softfriction material on their adjoining faces, as indicated. With the shaft48 removed from the frame the nut 49 may be removed, a member to betested such as a disc 2| may be placed on the shaft and clamped thereonby and-between the two nuts. A drum 50, preferably small in diameterrelatively to the diameand having no master diameter of its own, or none.of appreciable effect, is rigidly mounted on the shaft 48 about midwayof one-half of the portion thereof within the frame. An inextensible,flexible cord, wire or tape 5| is wrapped one or more times about thedrum and attached at its ends tautly to hooked rods 52 and 53 mounted tobe freely slidable in opposite ends of the frame. Coil springs 54 and 55respectively tend to keep the cord. 5| taut and the hooks urgedoutwardly. Each hook has a transverse bar, 56 and 5! respectively,extending inwardly into engagement with a pointer button, 58 and 59respectively, slidable in a corresponding slot, 60 and BI, in the stubshafts 4| and 42 respectively and associated in indicating relationshipwith ascale, 62 and 63, on the corresponding shaft. Counterweights 64and 65 are provided to counterbalance the hooks and their associatedparts; and a removable dummy drum 56 to counterbalance the drum 50.

With all elements in the position shown in Fig. 6, the scale readingsare noted, and the frame 40 revolved at a suitable speed for a minute ortwo and stopped. If there is a master diameter in the disc 2|, it willhave rotated the disc one way or the other during the revolution of theframe, and so will have moved one of the pointers 58 and 59, against theeffect of. the corresponding spring 54 or 55. The nuts 48 and 49 areloosened, the disc turned a specified fraction of a turn, the nutstightened again, and the operation repeated. From the results of a setof such operations, the position of the master diameter can bedetermined and the radius of gyration and the value of its excess massdetermined, 1. e. the mass required to be removed from the masterdiameter at the calculated radius on each side of its center to annulthe master characterof the diameter and remove the master diametereffect from the member.

It is believed to be self -evident from Fig. 6, that if, when theapparatus there shown is brought to a stop after having been revolvedabout the axis of the shafts 4| and 42 at-a known maximum speed, thereis recorded, say by the pointer 59, a

displacement to the left of this pointer, then there must have beenexerted upon the drum 50 at the moment of maximum speed of the'frame 40a is known. Letting the radius of the drumlbe r and the force indicatedon the scale 63 be 3; the torque indicated is then fr pound-feet.- Sincethe master diameter tends to turn the disk counterclockwise, the masterdiameter must lie in the upper right and lower left quadrants of thediskat an unknown angle a to the axis of the shafts '4! and 42. Assume thatthe excess mass ofthe master diameter is 2W and is evenly distributedalong the length of the diameter. It may then be treated as if half of2Wwere concentrated at 'each of the two midpoints of the radii composingthe diameter. Let the radial distance of such a midpoint be R. Then byformulae of rotary motion to be found in any'elementary text onmechanics, it can be shown that 2! during the rotation of the frame 136,as indicated alsoon the scale 63. All the quantities in this equationare known except W and a". Let the experiment be made twice withdiiferent maximum rotary speeds of the frame 46. Then there will berecorded two difierent angular displacements of the disk (each measuredand therefore known) and two difierent values of 1 (each measured andtherefore known). Substituting these in the formula above for n, b and,f respectively, two equations are obtained which can be solved for Wand a". This value of a-locates the position of the master diameter inthe disk as it stands in the apparatus. The corresponding value of W isthe mass of material to be removed from about the midpoint of eachradius of the master diameter, or to be added at about the midpoint ofeach radius of the diameter perpendicular to the master diametenror tobe compensated otherwise.

It is believed to be easily deducible from the above considerations thatthe simultaneously rotatable and revoluble member in question need notbe a simple circular disc to exhibit the master diameter efiect and tobe correctible to remove it. A four-armed right-angled cross, a star orthe like of any number of equally spaced, similarlyshaped rays, anyequal sided and equalangled polygon, are all illustrations ofconfigurations of such members which may be in static and dynamicbalance about their axes of rotation and still may be afiected with themaster diameter effect disclosed.

While the invention is disclosed and described as illustrated by a padsupport in a cable taping machine, it is not so limited, but appears tobe applicable-wherever a member is to be simultaneously rotated andrevolved at speeds suflicient to make master diameter eflect phenomenaappear.

The embodiments herein disclosed are illustrative and may be variouslymodified and departed from without departing from the spirit and scopeof the invention as pointed 'out in and limited only by the appendedclaims;

What is claimed is: 1. The method of correcting master diameterunbalance in a member adapted to be rotated about one axis while beingrevolved at high speed about an axis not parallel to the first namedaxis, which method comprises steps of revolving the member about an axisnot parallel to an axis of free rotation of the member and therebycreating in the member a force tending to set the master diameter of themember in a plane perpendicular to the said axis of revolution by motionabout the said axis of free rotation, measuring the moment of the saidforce, calculating therefrom the position of the said diameter" and theexcess mass therealong, and modifying the distribution of mass in themember to annul the said force.

2. The method of correcting master diameter unbalance in'a memberadapted to be rotated about one axis while being revolved at high speedabout an axis at right angles'to the first named axis, which methodcomprises steps of revolving the member about an axis at right angles toan axis of free rotation of the member and thereby creating in themember a force tending to set the master diameter of the member in aplane perpendicular to the said axis of revolution by motion about thesaid axis of free rotation, measuring the moment of the said force,calculating therefrom the position of the said diameter and the excessmass therealong, and modifying the distribution of mass in the member toannul the said force..

3. Apparatus to determine the position and excess mass of the masterdiameter of a member adapted for simultaneous revolution and rotationabout non-parallel axes, which apparatus comprises means to support themember to be freely rotatable about its axis of rotation, means torevolve the said supporting means and therewith the member about an axisnot parallel to the axis of rotation of themember and thereby to createa force thereintending to set the master diameter in a plane at rightangles to the axis of revolution, and means to measure the moment of thesaidio'rce.

4. Apparatus to determine the position and excess mass ofthe masterdiameter of a member adapted for simultaneous revolution and rotationabout axes at right angles to each other, which apparatus comprisesmeans to support the member to be freely rotatable about its axis ofrotation, means to revolve thesaid supporting means and therewith themember about an axis at right angles to the axis of rotation of themember and thereby'to create a force therein tending to set the masterdiameter in a plane at right angles to the axis of revolution, and meansto measure the moment of the said force. a

ELLWOOD W. REYNOLDS.

